Research
Research
My research lies at the intersection of nonlinear partial differential equations, fluid mechanics, thermodynamics, and multiscale dynamical systems. A central theme of my work is the interaction between geometric methods from dynamical systems and analytical techniques for PDE. I am particularly interested in problems with multiple scales, fast-slow structure, phase separation, diffusion, and chemical reactions.
This research project focuses on pattern formation in dryland ecosystems, where vegetation often appears in stripes or spots due to interactions between plants, water, and climate. Using reaction-diffusion models such as the Klausmeier model, I study how environmental change can trigger transitions such as desertification. A central goal is to extend geometric singular perturbation theory to infinite-dimensional systems described by partial differential equations. This will provide new tools for analyzing bifurcations, seasonal effects, and spatial heterogeneity in ecology and related areas.
DFG- Project number 571660837
A major part of my current research, developed in collaboration with Christian Kuehn and others, concerns the extension of geometric singular perturbation theory to infinite-dimensional systems. In this setting, I study the existence, persistence, and approximation of slow manifolds for PDE with fast-slow structure.
This perspective is especially useful for reaction-diffusion and cross-diffusion systems, where singular perturbation methods can reveal reduced dynamics while retaining essential features of the underlying model. I am interested both in the abstract theory and in applications to models arising in ecology, biochemistry, and reactive transport.
Representative topics include:
A Generalized Fenichel Theory in general infinite-dimensional Banach spapces,
Slow manifolds and their construction for fast-reaction systems,
applications to models such as SKT- and Michaelis-Menten-type systems, with cross-diffusion limits,
applications to Fokker-Planck equations.
Another central direction of my research, which was the focus of my PhD research under the supervision of Prof. Liu, concerns thermodynamically consistent continuum models in fluid dynamics and materials science. In particular, I study how temperature and entropy influence the modeling and analysis of PDE arising in diffuse-interface models, phase transitions, and chemically reacting flows.
My work in this area combines modeling, derivation, and rigorous analysis. The goal is to develop mathematically well-posed models that remain consistent with physical principles such as the second law of thermodynamics, and to analyze the resulting systems using modern tools from PDE and functional analysis.
Representative topics include:
non-isothermal diffuse-interface models,
temperature-dependent reaction-diffusion systems,
phase transition and interface evolution,
thermodynamically consistent fluid models.